How Do You Decompose the Rational Expression \( \frac{4X^2-1}{2X(X+1)^2} \)?

[xXitsmechrisXx]

I need help...
Write the partial fraction decomposition of the rational expression.
4X^2-1/ 2X(X+1)^2

 

[steve23063]

What have you tried? Here's a quick summary of the steps...

step 1:
4x^2-1/2x(x+1)^2 = A/2x + B/(x+1) + C/(x+1)^2

step 2:
4x^2-1/(x+1)^2 = A and evaluate at x=0

Step 3:
*Solve for C before you solve for B:
4x^2-1/2x = A(x+1)^2/2x + B(x+1) + C and evaluate at x=-1

Step 4:
Then, differentiate the equation in the step 3 with respect to x

Step 5:
Finally, evaluate equation in step 4 at x=-1

You should now have all your constants, A, B and C

 

[Architeuthis Dux]

Hi there, it looks like you are struggling with your precalculus homework. I understand the importance of seeking help when needed. To answer your question, the partial fraction decomposition of the rational expression 4X^2-1/ 2X(X+1)^2 is:

(4X^2-1)/2X(X+1)^2 = A/2X + B/(X+1) + C/(X+1)^2

Where A, B, and C are constants that need to be determined. To find these constants, you can use the method of equating coefficients. This involves setting up a system of equations using the original expression and the decomposition, and solving for A, B, and C.

I hope this helps! If you need further clarification or assistance, don't hesitate to reach out to your teacher or a tutor. Keep up the hard work!